Half-liberated manifolds, and their quantum isometries

TL;DR

This paper explores the half-liberation operation on algebraic submanifolds of complex spheres and computes the affine quantum isometry group for the sphere after this transformation.

Contribution

It introduces and analyzes the half-liberation operation on submanifolds of complex spheres and determines the quantum isometry group for the transformed sphere.

Findings

Defined the half-liberation operation for submanifolds of complex spheres.

Computed the affine quantum isometry group for the half-liberated sphere.

Provided multiple constructions of the half-liberation correspondence.

Abstract

We discuss the half-liberation operation $X\to X^*$, for the algebraic submanifolds of the unit sphere, $X\subset S^{N-1}_\mathbb C$. There are several ways of constructing this correspondence, and we take them into account. Our main results concern the computation of the affine quantum isometry group $G^+(X^*)$, for the sphere itself.